In general wireless LAN communication, an access point installed at public facilities or at home is connected through a broadband line with an external device or a network, and a session is set up between a communication terminal with a wireless LAN function and the foregoing access point, whereby the communication terminal can perform communication with the external device or the network. Examples of the communication terminal with the wireless LAN function include a personal computer, a game machine, a cell phone, a household electrical appliance, and so on. Patent Literature 1 below discloses, as a specific example of such communication, a home appliance network system consisting of an external device, a home gateway connected via the Internet with the external device, and a household electrical appliance to perform wireless communication under the home gateway.